Question 1443
y = -3x(squared) I need to find out the vertex, roots, if opens upward or downward, different points in order to graph parabola, and using the quadratic equation for something. 
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Make a table of values.  choose x = -2, -1, 0, 1 and 3
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Substitute -2 for x in y = -3x²
y = -3x²
y = -3(-2)²
y = -3(4)
y = -12
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So one point is (-2, -12). Plot that point.
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Substitute -1 for x in y = -3x²
y = -3x²
y = -3(-1)²
y = -3(1)
y = -3
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So another point is (-1, -3). Plot that point.
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Substitute 0 for x in y = -3x²
y = -3x²
y = -3(0)²
y = -3(0)
y = 0
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So another point is (0, 0). Plot that point. 
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Substitute 1 for x in y = -3x²
y = -3x²
y = -3(1)²
y = -3(1)
y = -3
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So another point is (1, -3). Plot that point.
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Substitute 2 for x in y = -3x²
y = -3x²
y = -3(2)²
y = -3(4)
y = -12
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So another point is (2, -12). Plot that point.
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Now when you connect these points you get
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{{{graph(200, 200, -4, 4, -13, 2, -3x^2)}}}
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The vertex is the turning point (at the top. It is (0,0)
Its root(s) is(are) found by setting y=0 ands solving for x.
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y = -3x²
0 = -3x²
3x² = 0
x² = 0
x = 0
So the only root is 0. 
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You can see that it opens downward, which will always be the case
if the coefficient of x² is negative.

I don't understand "using the quadratic equation for something." 

Edwin